But her new album, “Utopia,” prizes airiness : the breath that powers voices and flutes ; the atmosphere where birds fly ; structures and tempos that change freely rather than being locked to a beat. The album, due on Nov. 24, is the latest iteration of Björk’s career-long fascination with how nature and technology can interact.

In an interview at her apartment in Brooklyn, she said “Utopia” had long been her working title for the album. While making it, she read extensively about utopias : in academic studies and in stories and novels through the centuries, from ancient fables to the science fiction of Octavia E. Butler. “Utopia has gone from everything being monasteries, to feminist islands, to socialism, to ‘Peach Blossom Spring,’” she said, referring to a tale of an isolated, idyllic community that was written in the fifth century in China.

The 2016 election of Donald J. Trump only strengthened her determination to envision hope. “If optimism ever was like an emergency, it’s now,” she said. “Instead of moaning and becoming really angry, we need to actually come up with suggestions of what the world we want to live in, in the future, could be. This album is supposed to be like an idea, a suggestion, a proposal of the world we could live in.”

Björk’s proposal involves “that feeling, post-Trump, when everything’s gone horribly wrong,” she said. “And you escape to an island, and there’s a lot of women there with children, and everybody’s playing flutes, and everybody’s naked, and there’s all these plants you’ve never seen before and all these birds you’ve never heard before, and orchids, and it has that feeling of pioneering into a new world.”

Björk, 51, played a nearly finished version of the album for me during one of her brief stays in New York City this year, on a muggy day back in July. (She has since been to London, to her home in Iceland, and on tour to Moscow, Buenos Aires and Tbilisi, juggling concerts with her band, gigs as a disc jockey and curating Björk Digital, a traveling exhibition of her virtual-reality videos, which she will expand with songs from “Utopia.”) That afternoon, she was outfitted in a multicolored dress with an asymmetrical cut. After playing through the album on her stereo, she conversed volubly about the music across her kitchen table, over cups of strong coffee.

“I started thinking about this album as graffiti in the clouds,” she said. “It doesn’t have gravity. It’s more like floating in the air.”

The album concludes with “Future Forever,” with shimmering chords and Björk’s voice floating above silences ; she invokes a benign matriarchy. “Imagine a future and be in it/feel this incredible nurture, soak it in,” she sings, then turns to tech advice. “Your past is a loop — turn it off.”

But Björk has been ruminating on the past in the wake of the sexual misconduct allegations against Harvey Weinstein and others, and has decided to reckon with it. In a recent telephone call, she addressed an episode from her life that she had decided to air. In October, she posted on Facebook that she had faced unwanted touches and sexual advances from a “Danish director” : clearly Lars von Trier, who directed her in the 2000 film “Dancer in the Dark.” “I don’t want to be self-important in this,” Björk said on the phone from Iceland. “There are women out there that got it way worse than me.”

But when reading about Mr. Weinstein, she said, she was struck by “how he used the media against the ladies.” Stories had circulated at the time of filming that Björk was “difficult” on the set. But she said : “I was very conscientious. I showed up for every shoot on time,” until there was a dispute over control of her music.

“When I talked about this project with Lars, he always promised me I had full control of my music,” she said. “But I was turning up at dance rehearsals, and somebody else had been editing my music in a way that was totally musically wrong. And they would keep telling me, ‘Oh, it belongs to us now, it’s not yours.’

“After two months of just turning up for every single thing, and really just accepting all the harassment and just becoming part of the whole — just keeping on doing what I was told, basically — I had one weekend where I stood up. I could stand up as a musician and say, ‘I’m not returning back to work on Monday unless I get full control of my music.’ And that took one day. On Monday night, they said yes, and then on Tuesday, I returned to work.”

After Björk’s Facebook posts, Mr. von Trier’s assistant told Rolling Stone, “Lars declines the accusations Björk has made, but doesn’t wish to comment any further.” The Guardian reported that Mr. von Trier had told a Danish newspaper that he had not sexually harassed her. “That was not the case,” he told the newspaper, Jyllands-Posten. “But that we were definitely not friends, that’s a fact.” Attempts to reach Mr. von Trier for comment for this article received no response.

Björk described a far happier working environment during the making of “Utopia.” Like “Vulnicura,” the new album barely resembles music for pop radio playlists or dance clubs. It’s often dense and disorienting, with contending layers of vocals, flutes and percussive sounds. The songs are akin to chamber music and to the electronic experimentation of Björk’s collaborator throughout the album, the electronic musician Arca (Alejandro Ghersi), who grew up on Björk’s music. “He knew my back catalog better than I did,” she said.

Arca, who has also worked on tracks for Kanye West and the R&B singer Kelela, joined Björk partway through the making of “Vulnicura,” and went on to tour with her amid his own prolific solo efforts.

While Björk’s many previous co-producers have been enlisted to help execute her ideas, “Utopia” is closer to a full partnership. “What was different was that me and Alejandro were merging,” Björk said. “We felt like we could write 50 albums, because it was so fun. At first we were really surprised because the generational gap is pretty large between us, and then we figured out that philosophically, we share a lot of things. And there’s an optimistic and a celebrational element in both of our music that we really like.”

Arca gently steered her toward his favorite lesser-known Björk tracks, both instrumentals : “Ambergris March,” from her score for “Drawing Restraint 9,” and “Batabid,” a B side from 2001. There are echoes of them in her new songs. “He was mirroring back to me a side of me that I probably would have ignored,” Björk said. Meanwhile, for the bird calls she wanted, Björk chose species recorded in Arca’s home country, Venezuela.

“We were sending each other a thousand ideas — it was like playing games with someone,” Björk said. “It’s so interesting to communicate on so many levels. I was telling him, when I was being a music nerd at the beginning of this album : ‘If we are going to merge as two musicians, let’s go out of the grid. Let’s try to not do the normal song structure thing, but meet in a very instrumental way. Let’s have freedom.’”

Björk has often based an album on a particular sonic palette : strings for “Vulnicura,” the human voice for “Medulla,” the angelic, staccato sounds of harps, celesta and music boxes for “Vespertine.” For “Utopia,” Björk turned to the flute, the instrument she played growing up. “My flute side has been dormant for a long time,” she said.

To record the music she had composed on her computer, Björk gathered an ensemble of a dozen flutists, all women, for “Flute Fridays” in Reykjavik. “I tried to get as many colors out of the flutes as possible,” she said. “I miked them differently. Sometimes I had 12 flutes, sometimes six. There was alto flute, bass flute, tenor flute. They’re treated a lot, with a lot of effects, or they’re really clean, with nothing on them.

“We went between the churches in Reykjavik, trying to get the right sound,” she added. “Plus, I recorded a lot of the flutes in my cabin by the lake — trying to create this world where you have people hanging out in your living room, playing flutes and singing and making beats, but it’s part of real life.”

The hinge between “Vulnicura” and “Utopia” is “The Gate,” which Björk has released as the new album’s first single and as a kaleidoscopic video clip, awash in computer graphics yet somehow pastoral as well. She sings about the healing of the chest wound she showed on the cover of “Vulnicura,” and its turning into a gateway for love, as the song rises to a fervent refrain : “I care for you, care for you.” Another “manifesto,” Björk said, is “Body Memory” ; in its verses she overthinks herself into predicaments, only to be saved, in the choruses, by her instincts.

Her new songs also take up the more immediate pleasures of music and burgeoning romance. In “Blissing Me,” she sings about “two music nerds obsessing,” falling in love by “sending each other MP3s.” In “Courtship,” she looks into software-assisted dating. “He turned me down/I then downturned another/who then downturned her,” she sings, over chords built from flutes, and bursts of sputtering percussion hinting distantly at techno.

There’s still some lingering resentment and sorrow in songs like the defiant “Sue Me” and “Tabula Rasa,” and broader thoughts of solace in “Loss,” an elegiac melody strafed by a frenetic beat. But Björk wanted the album to look ahead. “‘Vulnicura’ was the end of a chapter, and this is the beginning of a new chapter,” she said.

“You go through different periods in your life. It would be really nice if we could just figure out one recipe that would work throughout our whole lives. But fortunately, or unfortunately, depending on how you look at it, most things don’t last long, and you have to rethink things, whether it’s practical or emotional or spiritual or whatever level it has to be.

“In the beginning of each period, you have to dream. You have to say, ‘Oh, I want …,’ and it might at the beginning sound very utopian. But then if half of it becomes real, that’s pretty good going. But you have to come up with, OK, what do I want to do next ?”

As the summer interview wound down, the afternoon suddenly darkened ; there was a rumble of thunder, and a heavy downpour began. Björk smiled to hear it. “All the tension has broken,” she said.